Islamic Finance is a financial system based on Islamic principles of transactions, offering alternatives to traditional forms of ethical and social financial behavior. Islamic banks started a rapid growth after the global financial crisis of 2008, showing greater resilience to risk than traditional banking institutions. Islamic banking is a normative concept that can be defined as banking compatible with the system of Islamic values. Today there are more than 300 Islamic banks in the world. Despite the significant growth observed in the assets of Islamic banks, their share in the global financial market is relatively small. A significant trend is the active penetration of Islamic banks into the national economies of the developed and developing countries, especially in the economies of countries that are seriously underfunded. The article describes the main trends, as well as the problems that prevent the expansion of Islamic banking in the modern economy. The authors conclude that Islamic banking faces such restrictions and limitations as: not relevant national banking legislation, lack of necessary financial infrastructure, low level of individual and corporative financial literacy, lack of information about Islamic financial products.